Video Transcript
If 𝑎 is equal to the square root of three and 𝑏 is equal to the square root of two, find the value of 𝑎 squared plus 𝑏 squared.
In this question, we are given the values of 𝑎 and 𝑏 and asked to evaluate an algebraic expression involving 𝑎 and 𝑏. To evaluate this expression, we need to start by substituting the values of 𝑎 and 𝑏 into the expression. Substituting 𝑎 is equal to the square root of three and 𝑏 is equal to the square root of two gives us 𝑎 squared plus 𝑏 squared is equal to the square root of three squared plus the square root of two squared.
We can then recall that the square root of a nonnegative number 𝑐 is the nonnegative number whose square is 𝑐. So, the square root of 𝑐 all squared is just equal to 𝑐. Therefore, the square root of three squared is equal to three, and the square root of two squared is equal to two. This gives us three plus two, which we can calculate is equal to five.
Hence, if 𝑎 is equal to the square root of three and 𝑏 is equal to the square root of two, then 𝑎 squared plus 𝑏 squared is equal to five.
